Choose the odd number: 121, 169, and 289 are squares of primes (11^2, 13^2, 17^2). One number is the square of a composite (15^2). Identify that odd square.
Verbal Reasoning
Classification
Difficulty: Easy
Choose an option
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A121
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B169
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C225
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D289
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ENone of these
Answer
Correct Answer: 225
Explanation
Introduction / Context:All four are perfect squares, but three are squares of primes while one is the square of a composite integer, making it the odd one out.
Given Data / Assumptions:
- 121 = 11^2 (prime base).
- 169 = 13^2 (prime base).
- 289 = 17^2 (prime base).
- 225 = 15^2 (composite base; 15 = 3 * 5).
Concept / Approach:Classify by the nature of the base whose square forms the number: prime versus composite.
Step-by-Step Solution:
Identify bases: 11, 13, 15, 17.Check primality of each base: 11, 13, 17 are prime; 15 is composite.Therefore, 225 is distinct as a square of a composite.Verification / Alternative check:Factor 225 = 15 * 15 = (3 * 5) * (3 * 5) = 3^2 * 5^2; the base 15 is not prime.
Why Other Options Are Wrong:121, 169, and 289 are squares of prime bases, matching the majority rule.
Common Pitfalls:Assuming all squares are alike without considering the primality of the base.
Final Answer:225 is the odd square (square of a composite).